WASHINGTON — Democrats are counting on New England to help them pick up Republican-held Senate seats on Nov. 6 and construct a barrier against losses in Nebraska and elsewhere that could erase their majority.

The National Republican Senatorial Committee has stopped spending money in Maine, where former Governor Angus King, an independent, leads in the polls and is viewed as probable to side with Democrats if he wins.

In Massachusetts, Republican Senator Scott Brown faces a strong challenge from Elizabeth Warren, a Democrat, as the state is poised to easily support President Obama over Mitt Romney.

Republican hopes of taking the seat in Connecticut are fading. Democratic Representative Chris Murphy has steadied his campaign against former wrestling executive Linda McMahon, who spent $50 million on an unsuccessful bid in 2010 and $42.6 million and counting this year. McMahon’s less-than-stellar debate performances and the state’s Democratic tilt have undercut the Republican candidate’s prospects.

‘‘If New England could tip the Senate’s balance to the Republicans, it would be fairly earth-shattering,’’ said Rob Gray, a veteran GOP consultant in Massachusetts. ‘‘The real question is whether these races will be close-but-no-cigar for Republicans.’’

In Senate math, the loss of two seats in New England complicates the GOP calculation for majority control. Republicans would have to gain a net of six seats while holding suddenly uncertain Indiana, or a net of five seats if Romney wins the presidency. Democrats currently have the edge, 53 to 47, including two independents who caucus with the party.

There are 23 Democratic seats and 10 Republican seats on this year’s ballots.

Republicans are optimistic they can make it add up and they point to fresh enthusiasm for Romney and the party ticket. After weeks of pure toss-ups, Republicans say North Dakota and Wisconsin are trending GOP though still close, Montana remains tight and the contest in Ohio has narrowed, due in large part to the roughly $20 million in negative ads against Democratic Senator Sherrod Brown.

In a late move, the Republicans invested $500,000 in Pennsylvania, where some polls show a tight race between first-term Senator Bob Casey and Tea Party-backed businessman Tom Smith, who has invested more than $16 million in his bid. The state has been considered safely Democratic for much of the year.

Republicans and Democrats expect Nebraska to switch to the GOP despite the candidacy of former Senator Bob Kerrey, and Virginia to stay close, with the outcome of the presidential election crucial to the final count.

That’s not so in Florida. Romney has grabbed a slight lead in polls, but there are no signs that it has helped Republican Representative Connie Mack in his race to unseat a two-term Democrat, Senator Bill Nelson. In the most telling development, outside Republican groups bailed on the Senate race at the beginning of October and there is no indication they will resume spending in the closing days.

Privately, Republicans fret about Indiana, unsure about the political damage from Republican state treasurer Richard Mourdock’s debate comment that pregnancy resulting from rape is ‘‘something God intended.’’